Investment philosophies by aswath damodaran

Investment philosophies by aswath damodaran Investment philosophies by aswath damodaran Investment philosophies by aswath damodaran Investment philosophies by aswath damodaran

CHAPTER 1 INTRODUCTION

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CHAPTER 2 UPSIDE, DOWNSIDE: UNDERSTANDING RISK

Risk is part of investing and understanding what it is and how it is measured

is essential to developing an investment philosophy In this chapter, we will lay the

foundations for analyzing risk in investments We present alternative models for measuring

risk and converting these risk measures into an expected return We will also consider ways

in an investor can measure his or her risk aversion

We begin with a discussion of risk and present our analysis in three steps In the first step,

we define risk in terms of uncertainty about future returns The greater this uncertainty, the

more risky an investment is perceived to be The next step, which we believe is the central

one, is to decompose this risk into risk that can be diversified away by investors and risk

that cannot In the third step, we look at how different risk and return models in finance

attempt to measure this non-diversifiable risk We compare and contrast the most widely

used model, the capital asset pricing model, with other models, and explain how and why

they diverge in their measures of risk and the implications for the equity risk premium In

the second part of this chapter, we consider default risk and how it is measured by ratings

agencies In addition, we discuss the determinants of the default spread and why it might

change over time

What is risk?

Risk, for most of us, refers to the likelihood that in life’s games of chance, we will

receive an outcome that we will not like For instance, the risk of driving a car too fast is

getting a speeding ticket, or worse still, getting into an accident Webster’s dictionary, in

fact, defines risk as “exposing to danger or hazard” Thus, risk is perceived almost entirely

in negative terms

In finance, our definition of risk is both different and broader Risk, as we see it,

refers to the likelihood that we will receive a return on an investment that is different from

the return we expected to make Thus, risk includes not only the bad outcomes, i.e, returns

that are lower than expected, but also good outcomes, i.e., returns that are higher than

expected In fact, we can refer to the former as downside risk and the latter is upside risk;

but we consider both when measuring risk In fact, the spirit of our definition of risk in

finance is captured best by the Chinese symbols for risk, which are reproduced below:

The first symbol is the symbol for “danger”, while the second is the symbol for

“opportunity”, making risk a mix of danger and opportunity It illustrates very clearly the

tradeoff that every investor and business has to make – between the higher rewards that

come with the opportunity and the higher risk that has to be borne as a consequence of the

danger

Much of this chapter can be viewed as an attempt to come up with a model that best

measures the “danger” in any investment and then attempts to convert this into the

“opportunity” that we would need to compensate for the danger In financial terms, we

term the danger to be “risk” and the opportunity to be “expected return”

Equity Risk and Expected Return

To demonstrate how risk is viewed in finance, we will present risk analysis in three

steps First, we will define risk Second, we will differentiate between risk that is specific to

one or a few investments and risk that affects a much wider cross section of investments

We will argue that in a market where investors are well diversified, it is only the latter risk,

called market risk that will be rewarded Third, we will look at alternative models for

measuring this market risk and the expected returns that go with it

I Defining Risk

Investors who buy assets expect to earn returns over the time horizon that they hold

the asset Their actual returns over this holding period may be very different from the

expected returns and it is this difference between actual and expected returns that is source

of risk For example, assume that you are an investor with a year time horizon buying a

1-year Treasury bill (or any other default-free one-1-year bond) with a 5% expected return At

the end of the 1-year holding period, the actual return on this investment will be 5%, which

is equal to the expected return The return distribution for this investment is shown in

Figure 2.1

This is a riskless investment.

To provide a contrast to the riskless investment, consider an investor who buys stock

in a company like Cisco This investor, having done her research, may conclude that she can

make an expected return of 30% on Cisco over her 1-year holding period The actual return

over this period will almost certainly not be equal to 30%; it might be much greater or much

lower The distribution of returns on this investment is illustrated in Figure 2.2

In addition to the expected return, an investor has to note that the actual returns, in this case,

are different from the expected return The spread of the actual returns around the expected

return is measured by the variance or standard deviation of the distribution; the greater the

deviation of the actual returns from expected returns, the greater the variance

One of the limitations of variance is that it considers all variation from the expected

return to be risk Thus, the potential that you will earn a

60% return on Cisco (30% more than the expected return of

30%) affects the variance exactly as much as the potential

that you will earn 0% (30% less than the expected return)

In other words, you do not distinguish between downside

and upside risk This is justified by arguing that risk is

symmetric – upside risk must inevitably create the potential

for downside risk.1 If you are bothered by this assumption,

you could compute a modified version of the variance, called

the semi-variance, where you consider only the returns that fall below the expected return.

It is true that measuring risk with variance or semi-variance can provide too limited a

view of risk, and there are some investors who use simpler stand-ins (proxies) for risk For

instance, you may consider stocks in some sectors (such as technology) to be riskier than

1 In statistical terms, this is the equivalent of assuming that the distribution of returns is close to normal.

The Most and Least Volatile Stocks: Take a look

at the 50 most and 50 leastvolatile stocks traded in theUnited States, based upon 5years of weekly data

stocks in other sectors (say, food processing) Others prefer ranking or categorization

systems, where you put firms into risk classes, rather than trying to measure its risk in units

Thus, Value Line ranks firms into five classes, based upon risk

There is one final point that needs to be made about how variances and

semi-variances are estimated for most stocks Analysts usually look at the past – stock prices over

the last 2 or 5 years- to make these estimates This may be appropriate for firms that have

not changed their fundamental characteristics – business or leverage – over the period For

firms that have changed significantly over time, variances from the past may provide a very

misleading view of betas in the future

II Diversifiable and Non-diversifiable Risk

Although there are many reasons that actual returns may differ from expected

returns, we can group the reasons into two categories: firm-specific and market-wide The

risks that arise from firm-specific actions affect one or a few investments, while the risk

arising from market-wide reasons affect many or all investments This distinction is critical

to the way we assess risk in finance

The Components of Risk

When an investor buys stock or takes an equity position in a firm, he or she is

exposed to many risks Some risk may affect only one or a few firms and it is this risk that

we categorize as firm-specific risk Within this category, we would consider a wide range of

risks, starting with the risk that a firm may have misjudged the demand for a product from

its customers; we call this project risk For instance, consider an investment by Boeing in a

new larger capacity airplane that we will call the Super Jumbo This investment is based on

the assumption that airlines want a larger airplane and will be willing to pay a higher price

for it If Boeing has misjudged this demand, it will clearly have an impact on Boeing’s

earnings and value, but it should not have a significant effect on other firms in the market

The risk could also arise from competitors proving to be stronger or weaker than

anticipated; we call this competitive risk For instance, assume that Boeing and Airbus are

competing for an order from Qantas, the Australian airline The possibility that Airbus may

win the bid is a potential source of risk to Boeing and perhaps a few of its suppliers But

again, only a handful of firms in the market will be affected by it Similarly, the Home

Depot recently launched an online store to sell its home improvement products Whether it

succeeds or not is clearly important to the Home Depot and its competitors, but it is unlikely

to have an impact on the rest of the market In fact, we would extend our risk measures to

include risks that may affect an entire sector but are restricted to that sector; we call this

sector risk For instance, a cut in the defense budget in the United States will adversely

affect all firms in the defense business, including Boeing, but there should be no significant

impact on other sectors, such as food and apparel What is common across the three risks

described above – project, competitive and sector risk – is that they affect only a small

sub-set of firms

There is other risk that is much more pervasive and affects many if not all

investments For instance, when interest rates increase, all investments are negatively

affected, albeit to different degrees Similarly, when the economy weakens, all firms feel the

effects, though cyclical firms (such as automobiles, steel and housing) may feel it more We

term this risk market risk.

Finally, there are risks that fall in a gray area, depending upon how many assets they

affect For instance, when the dollar strengthens against other currencies, it has a significant

impact on the earnings and values of firms with international operations If most firms in the

market have significant international operations, it could well be categorized as market risk

If only a few do, it would be closer to firm-specific risk Figure 2.3 summarizes the break

down or the spectrum of firm specific and market risks

Actions/Risk that

affect only one

firm

Actions/Risk that affect all investments

or weaker than anticipated

Entire Sector may be affected

by action

Exchange rate and Political risk

Interest rate, Inflation &

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Affects few firms

Affects many firms

Why Diversification reduces or eliminates Firm-specific Risk: An Intuitive Explanation

As an investor, you could invest your entire portfolio in one stock, say Boeing If

you do so, you are exposed to both firm specific and market risk If, however, you expand

your portfolio to include other assets or stocks, you are diversifying, and by doing so, you

can reduce your exposure to firm-specific risk There are two reasons why diversification

reduces or, at the limit, eliminates firm specific risk The first is that each investment in a

Highest R-squared companies: Take a look

at the 50 companies withthe highest proportion ofmarket risk using the last

5 years or weekly data

diversified portfolio is a much smaller percentage of that portfolio than would be the case if

you were not diversified Thus, any action that increases or decreases the value of only that

investment or a small group of investments will have only a small impact on your overall

portfolio, whereas undiversified investors are much more exposed to changes in the values

of the investments in their portfolios The second reason is that the effects of firm-specific

actions on the prices of individual assets in a portfolio can be either positive or negative for

each asset in any period Thus, in very large portfolios, this risk will average out to zero and

will not affect the overall value of the portfolio

In contrast, the effects of market-wide movements are likely to be in the same

direction for most or all investments in a portfolio, though

some assets may be affected more than others For instance,

other things being equal, an increase in interest rates will

lower the values of most assets in a portfolio Being more

diversified does not eliminate this risk

One of the simplest ways of measuring how much

risk in a firm is firm specific is to look at the proportion of

the firm’s price movements that are explained by the

market This is called the R-squared and it should range

between zero and one can be stated as a percentage; it measures the proportion of the firm’s

risk that comes from the market A firm with an R-squared of zero has 100% firm specific

risk whereas a firm with an R-squared of 0% has no firm specific risk

Why is the marginal investor assumed to be diversified?

The argument that diversification reduces an investor’s exposure to risk is clear both

intuitively and statistically, but risk and return models in finance go further The models

look at risk through the eyes of the investor most likely to be trading on the investment at

any point in time, i.e the marginal investor They argue that this investor, who sets prices for

investments, is well diversified; thus, the only risk that he or she cares about is the risk

added on to a diversified portfolio or market risk This argument can be justified simply

The risk in an investment will always be perceived to be higher for an undiversified investor

than for a diversified one, since the latter does not shoulder any firm-specific risk and the

former does If both investors have the same expectations about future earnings and cash

flows on an asset, the diversified investor will be willing to pay a higher price for that asset

because of his or her perception of lower risk Consequently, the asset, over time, will end

up being held by diversified investors

This argument is powerful, especially in markets where assets can be traded easily

and at low cost Thus, it works well for a stock traded in the United States, since investors

can become diversified at fairly low cost In addition, a significant proportion of the trading

in US stocks is done by institutional investors, who tend to be well diversified It becomes a

more difficult argument to sustain when assets cannot be easily traded, or the costs of

trading are high In these markets, the marginal investor may well be undiversified and

firm-specific risk may therefore continue to matter when looking at individual investments For

instance, real estate in most countries is still held by investors who are undiversified and

have the bulk of their wealth tied up in these investments

III Models Measuring Market Risk

While most risk and return models in use in finance agree on the first two steps of

the risk analysis process, i.e., that risk comes from the distribution of actual returns around

the expected return and that risk should be measured from the perspective of a marginal

investor who is well diversified, they part ways when it comes to measuring

non-diversifiable or market risk In this section, we will discuss the different models that exist in

finance for measuring market risk and why they differ We will begin with what still is the

standard model for measuring market risk in finance – the capital asset pricing model

(CAPM) – and then discuss the alternatives to this model that have developed over the last

two decades While we will emphasize the differences, we will also look at what they have in

common

A The Capital Asset Pricing Model (CAPM)

The risk and return model that has been in use the longest and is still the standard in

most real world analyses is the capital asset pricing model (CAPM) In this section, we will

examine the assumptions made by the model and the measures of market risk that emerge

from these assumptions

Assumptions

While diversification reduces the exposure of investors to firm specific risk, most

investors limit their diversification to holding only a few assets Even large mutual funds

rarely hold more than a few hundred stocks and many of them hold as few as ten to twenty

There are two reasons why investors stop diversifying One is that an investor or mutual

fund manager can obtain most of the benefits of diversification from a relatively small

portfolio, because the marginal benefits of diversification become smaller as the portfolio

gets more diversified Consequently, these benefits may not cover the marginal costs of

diversification, which include transactions and monitoring costs Another reason for limiting

diversification is that many investors (and funds) believe they can find under valued assets

and thus choose not to hold those assets that they believe to be fairly or over valued

The capital asset pricing model assumes that there are no transactions costs and that

all assets are traded It also assumes that everyone has access to the same information and

that investors therefore cannot find under or over valued assets in the market place Making

these assumptions allows investors to keep diversifying without additional cost At the limit,

each investor’s will include every traded asset in the market held in proportion to its market

value The fact that this diversified portfolio includes all traded assets in the market is the

reason it is called the market portfolio, which should not be a surprising result, given the

benefits of diversification and the absence of transactions costs in the capital asset pricing

model If diversification reduces exposure to firm-specific risk and there are no costs

associated with adding more assets to the portfolio, the logical limit to diversification is to

hold a small proportion of every traded asset in the market If this seems abstract, consider

the market portfolio to be an extremely well diversified mutual fund that holds stocks and

real assets, and treasury bills as the riskless asset In the CAPM, all investors will hold

combinations of treasury bills and the same mutual fund2

Investor Portfolios in the CAPM

If every investor in the market holds the identical market portfolio, how exactly do

investors reflect their risk aversion in their investments? In the capital asset pricing model,

investors adjust for their risk preferences in their allocation decision, where they decide how

much to invest in a riskless asset and how much in the market portfolio Investors who are

risk averse might choose to put much or even all of their wealth in the riskless asset

Investors who want to take more risk will invest the bulk or even all of their wealth in the

market portfolio Investors, who invest all their wealth in the market portfolio and are still

desirous of taking on more risk, would do so by borrowing at the riskless rate and investing

more in the same market portfolio as everyone else

These results are predicated on two additional assumptions First, there exists a

riskless asset, where the expected returns are known with certainty Second, investors can

lend and borrow at the same riskless rate to arrive at their optimal allocations While lending

at the riskless rate can be accomplished fairly simply by buying treasury bills or bonds,

borrowing at the riskless rate might be more difficult to do for individuals There are

variations of the CAPM that allow these assumptions to be relaxed and still arrive at the

conclusions that are consistent with the model

2 The significance of introducing the riskless asset into the choice mix, and the implications for portfolio

choice were first noted in Sharpe (1964) and Lintner (1965) Hence, the model is sometimes called the

Sharpe-Lintner model.

Highest and Lowest Beta Stocks: Take a look at

the 50 highest beta and 50lowest beta stocks traded

in the United States, basedupon 5 years of weeklydata

Measuring the Market Risk of an Individual Asset

The risk of any asset to an investor is the risk added by that asset to the investor’s

overall portfolio In the CAPM world, where all investors

hold the market portfolio, the risk to an investor of an

individual asset will be the risk that this asset adds on to

that portfolio Intuitively, if an asset moves independently

of the market portfolio, it will not add much risk to the

market portfolio In other words, most of the risk in this

asset is firm-specific and can be diversified away In

contrast, if an asset tends to move up when the market

portfolio moves up and down when it moves down, it will

add risk to the market portfolio This asset has more market risk and less firm-specific risk

Statistically, this added risk is measured by the covariance of the asset with the market

portfolio

The covariance is a percentage value and it is difficult to pass judgment on the

relative risk of an investment by looking at this value In other words, knowing that the

covariance of Boeing with the Market Portfolio is 55% does not provide us a clue as to

whether Boeing is riskier or safer than the average asset We therefore standardize the risk

measure by dividing the covariance of each asset with the market portfolio by the variance of

the market portfolio This yields a risk measure called the beta of the asset:

Beta of an asset =Covariance of asset with Market Portfolio

Variance of the Market PortfolioThe beta of the market portfolio, and by extension, the average asset in it, is one Assets that

are riskier than average (using this measure of risk) will have betas that are greater than 1

and assets that are less risky than average will have betas that are less than 1 The riskless

asset will have a beta of 0

Getting Expected Returns

Once you accept the assumptions that lead to all investors holding the market

portfolio and measure the risk of an asset with beta, the return you can expect to make can

be written as a function of the risk-free rate and the beta of that asset

Expected Return on an investment = Riskfree Rate + Beta (Risk Premium for

buying the average risk investment)

Consider the three components that go into the expected return

a Riskless Rate: The return you can make on a riskfree investment becomes the base from

which you build expected returns Essentially, you are assuming that if you can make 5%

investing in treasury bills or bonds, you would not settle for less than this as an expected

return for investing in a riskier asset Generally speaking, we use the interest rate on

government securities to estimate the riskfree rate, assuming that such securities have no

default risk While this may be a safe assumption in the United States and other developed

markets, it may be inappropriate in many emerging markets, where governments themselves

are viewed as capable of defaulting In such cases, the government bond rate will include a

premium for default risk and this premium will have to be removed to arrive at a riskfree

rate.3

b The beta of the investment: The beta is the only component in this model which varies

from investment to investment, with investments that add more risk to the market portfolio

having higher betas But where do betas come from? Since the beta measures the risk added

to a market portfolio by an individual stock, it is usually estimated by running a regression

of past returns on the stock against returns on a market index

Figure 2.4: Beta Estimate for Cisco: S&P 500

Slope of the line is beta

R squared measures how far points fall from regression line.

3 Consider, for example, a government bond issued by the Brazilian government Denominated in Brazilian

Real, this bond has an interest rate of 17% The Brazilian government is viewed as having default risk on

this bond and is rated BB by Standard and Poor’s If we subtract the typical default spread earned by BB rated

country bonds (about 5%) from 17%, we end up with a riskless rate in Brazilian Real of 12%.

Risk Premium for the United States: Take a look at

the equity risk premiumimplied in the U.S stockmarket from 1960 throughthe most recent year

The slope of the regression captures how sensitive a stock is to market movements and is

the beta of the stock In the regression above, for instance, the beta of Cisco would be 1.39

There are, however, two problems with regression betas One is that the beta comes with

estimation error – the standard error in the estimate is 0.27 Thus, the true beta for Cisco

could be anywhere from 85 to 1.93 – this range is estimated by adding and subtracting two

standard errors to the beta estimate The other is that

firms change over time and we are looking backwards

rather than looking forwards A better way to estimate

betas is to look at the average beta for publicly traded

firms in the business or businesses Cisco operates in

While these betas come from regressions as well, the

average beta is always more precise than any one firm’s

beta estimate

c The risk premium for buying the average risk

investment: You can view this as the premium you would demand for investing in equities as

a class as opposed to the riskless investment Thus, if you require a return of 9% for

investing in equities and the treasury bond rate is 5%, your risk premium is 4% There are

again two ways in which you can estimate this risk premium One is to look at the past and

look at the typical premium you would have earned investing in stocks as opposed to a

riskless investment This number is called a historical premium and yields about 5-7% for

the United States The other is to look at how stocks are priced today and to estimate the

premium that investors must be demanding This is called an implied premium and yields a

value of about 4% for U.S stocks in early 2002

Bringing it all together, you could use the capital asset pricing model to estimate the

expected return on a stock for Cisco for the future (assuming a treasury bond rate of 5%,

the regression beta of 1.39 and a risk premium of 4%):

Expected return on Cisco = T Bond Rate + Beta * Risk Premium

= 5% + 1.39 (4%) = 10.56%

What does this number imply? It does not mean that you will earn 10.56% every year from

risk, but it does provide a benchmark that you will have to meet and beat if you are

considering Cisco as an investment For Cisco to be a good investment, you would have to

expect it to make more than 10.56% as an annual return in the future

In summary, in the capital asset pricing model, all the market risk is captured in the beta,

measured relative to a market portfolio, which at least in theory should include all traded

assets in the market place held in proportion to their market value

Betas for Other Investments

Most services report betas for publicly traded stocks, but there is no reason why the

concept cannot be extended to other investments You could compute the beta of real estate,

gold or even fine art as an investment, just as you computed the beta for Cisco While

analysts have done this and concluded that both real estate and gold are low beta

investments (though not necessarily low variance investments), we would add a few

cautionary notes The first is that it is difficult to get traded prices on some alternative

investments on a continuous basis 4The second is that many analysts continue to use the

stock index as their measure of the market portfolio Since the market portfolio in the capital

asset pricing model is supposed to include all traded assets, this likely to give you betas that

are biased downwards for non-equity investments

If you modify the market portfolio to include other traded asset classes and compute

betas for alternative investments, you may even find some that have negative betas While,

on the face of it, this may seem absurd, you can get negative betas for investments that

reduce the risk (rather than add on to risk) of the market portfolio Essentially, these

investments act as insurance against some large component of market risk, going up as

other investments in the portfolio go down This is the reason why some analysts claim that

gold as an investment should have a negative beta, because it tends to do well when inflation

increases whereas financial investments are hurt

B Alternatives to the Capital Asset Pricing Model

The restrictive assumptions on transactions costs and private information in the

capital asset pricing model and the model’s dependence on the market portfolio have long

been viewed with skepticism by both academics and practitioners There are three

alternatives to the CAPM that have been developed over time:

1 Arbitrage Pricing Model: To understand the arbitrage pricing model, we need to begin

with a definition of arbitrage The basic idea is a simple one Two portfolios or assets with

the same exposure to market risk should be priced to earn exactly the same expected

returns If they are not, you could buy the less expensive portfolio, sell the more expensive

portfolio, have no risk exposure and earn a return that exceeds the riskless rate This is

arbitrage If you assume that arbitrage is not possible and that investors are diversified, you

can show that the expected return on an investment should be a function of its exposure to

market risk While this statement mirrors what was stated in the capital asset pricing model,

4 Analysts have tried to get around this problem by using the prices of real estate investment trusts which

are traded, but they represent a small fraction of all real estate investments.

the arbitrage pricing model does not make the restrictive assumptions about transactions

costs and private information that lead to the conclusion that one beta can capture an

investment’s entire exposure to market risk Instead, in the arbitrage pricing model, you can

have multiples sources of market risk and different exposures to each (betas) and your

expected return on an investment can be written as:

Expected return = Riskfree rate + Beta for factor 1 (Risk premium for factor 1) +

Beta for factor 2 (Risk premium for factor 2)….+ Beta for factor n (Risk premium

for factor n)

The practical questions then become knowing how many factors there are that determine

expected returns and what the betas for each investment are against these factors The

arbitrage model estimates both by examining historical data on stock returns for common

patterns (since market risk affects most stocks) and estimating each stock’s exposure to

these patterns in a process called factor analysis A factor analysis provides two output

measures:

1 It specifies the number of common factors that affected the historical return data

2 It measures the beta of each investment relative to each of the common factors and

provides an estimate of the actual risk premium earned by each factor

The factor analysis does not, however, identify the factors in economic terms – the factors

remain factor 1, factor etc In summary, in the arbitrage pricing model, the market risk is

measured relative to multiple unspecified macroeconomic variables, with the sensitivity of

the investment relative to each factor being measured by a beta The number of factors, the

factor betas and factor risk premiums can all be estimated using the factor analysis

2 Multi-factor Models for risk and return: The arbitrage pricing model's failure to

identify the factors specifically in the model may be a statistical strength, but it is an intuitive

weakness The solution seems simple: Replace the unidentified statistical factors with

specific economic factors and the resultant model should have an economic basis while still

retaining much of the strength of the arbitrage pricing model That is precisely what

multi-factor models try to do Multi-multi-factor models generally are determined by historical data,

rather than economic modeling Once the number of factors has been identified in the

arbitrage pricing model, their behavior over time can be extracted from the data The

behavior of the unnamed factors over time can then be compared to the behavior of

macroeconomic variables over that same period to see whether any of the variables is

correlated, over time, with the identified factors

For instance, Chen, Roll, and Ross (1986) suggest that the following

macroeconomic variables are highly correlated with the factors that come out of factor

analysis: industrial production, changes in default premium, shifts in the term structure,

unanticipated inflation, and changes in the real rate of return These variables can then be

correlated with returns to come up with a model of expected returns, with firm-specific betas

calculated relative to each variable

( )R R f GNP[E(R GNP) R f] I[E( )R I R f] [E( )R R f]

where

GNP = Beta relative to changes in industrial production

E(RGNP) = Expected return on a portfolio with a beta of one on the industrial

production factor and zero on all other factors

I = Beta relative to changes in inflation

E(RI) = Expected return on a portfolio with a beta of one on the inflation factor

and zero on all other factorsThe costs of going from the arbitrage pricing model to a macroeconomic multi-

factor model can be traced directly to the errors that can be made in identifying the factors

The economic factors in the model can change over time, as will the risk premia associated

with each one For instance, oil price changes were a significant economic factor driving

expected returns in the 1970s but are not as significant in other time periods Using the

wrong factor or missing a significant factor in a multi-factor model can lead to inferior

estimates of expected return

In summary, multi-factor models, like the arbitrage pricing model, assume that

market risk can be captured best using multiple macro economic factors and betas relative to

each Unlike the arbitrage pricing model, multi factor models do attempt to identify the

macro economic factors that drive market risk

3 Regression or Proxy Models: All the models described so far begin by defining market

risk in broad terms and then developing models that might best measure this market risk

All of them, however, extract their measures of market risk (betas) by looking at historical

data There is a final class of risk and return models that start with the returns and try to

explain differences in returns across stocks over long time periods using characteristics

such as a firm’s market value or price multiples5 Proponents of these models argue that if

some investments earn consistently higher returns than other investments, they must be

riskier Consequently, we could look at the characteristics that these high-return investments

5 A price multiple is obtained by dividing the market price by its earnings or its book value Studies

indicate that stocks that have low price to earnings multiples or low price to book value multiples earn

higher returns than other stocks.

have in common and consider these characteristics to be indirect measures or proxies for

market risk

Fama and French, in a highly influential study of the capital asset pricing model in

the early 1990s, noted that actual returns between 1963 and 1990 have been highly

correlated with book to price ratios6 and size High return investments, over this period,

tended to be investments in companies with low market capitalization and high book to price

ratios Fama and French suggested that these measures be used as proxies for risk and

report the following regression for monthly returns on stocks on the NYSE:

MV

t =1 77 % 0 11 ln( )+

where

MV = Market Value of Equity

BV/MV = Book Value of Equity / Market Value of Equity

The values for market value of equity and book-price ratios for individual firms, when

plugged into this regression, should yield expected monthly returns

A Composite of the CAPM and Proxy Models: Three Factor Models

The capital asset pricing model relates the expected return on an investment to its

beta against a market portfolio The proxy models find that there are other variables such as

market capitalization and price to book ratios explain returns better than betas There are

composite models that attempt to blend the two and estimated expected returns as a function

of betas, market capitalization and price to book ratios These are also called factor models

Will these composite models work better than the CAPM? Of course! Should we

therefore use them instead of the CAPM? The answer is that it depends on what you are

trying to do If you are trying to explain the past performance of portfolio managers, it may

make sense to use composite models, since failing to do so will make portfolio managers

who invest in small cap stocks look much better than portfolio managers who invest in large

cap stocks If you are trying to estimate expected returns for the future, to make judgments

on where to invest your money, you should be careful about going down this road, since it

seems designed to lead the conclusion that everything is fairly priced Consider why If

there are pockets of the market which are systematically mispriced – say small cap stocks

with low price to book ratios – you want to buy these stocks and you will using a

conventional risk and return model If you use a composite model and include market

capitalization and price to book ratios as factors, these same stocks will look fairly valued

6 The book to price ratio is the ratio of the book value of equity to the market value of equity.

A Comparative Analysis of Risk and Return Models

Figure 2.5 summarizes all the risk and return models in finance, noting their

similarities in the first two steps and the differences in the way they define market risk

Figure 2.5: Risk and Return Models in Finance

The risk in an investment can be measured by the variance in actual returns around an

Can be diversified away in a diversified portfolio Cannot be diversified away since most assets

1 each investment is a small proportion of portfolio are affected by it.

2 risk averages out across investments in portfolio

The marginal investor is assumed to hold a “diversified” portfolio Thus, only market risk will

be rewarded and priced.

If there is

1 no private information

2 no transactions cost

the optimal diversified

portfolio includes every

traded asset Everyone

will hold this market portfolio

Market Risk = Risk

added by any investment

to the market portfolio:

If there are no arbitrage opportunities then the market risk of any asset must be captured by betas relative to factors that affect all investments.

Market Risk = Risk exposures of any asset to market factors

Beta of asset relative to

Market portfolio (from

a regression)

Betas of asset relative

to unspecified market factors (from a factor analysis)

Since market risk affects most or all investments,

it must come from macro economic factors.

Market Risk = Risk exposures of any asset to macro economic factors.

Betas of assets relative

to specified macro economic factors (from

a regression)

In an efficient market, differences in returns across long periods must

be due to market risk differences Looking for variables correlated with returns should then give

us proxies for this risk.

Market Risk = Captured by the Proxy Variable(s)

Equation relating returns to proxy variables (from a regression)

Step 1: Defining Risk

Step 2: Differentiating between Rewarded and Unrewarded Risk

Step 3: Measuring Market Risk

As noted in Figure 2.5, all the risk and return models developed in this chapter make

some assumptions in common They all assume that only market risk is rewarded and they

derive the expected return as a function of measures of this risk The capital asset pricing

model makes the most restrictive assumptions about how markets work but arrives at the

simplest model, with only one factor driving risk and requiring estimation The arbitrage

pricing model makes fewer assumptions but arrives at a more complicated model, at least in

terms of the parameters that require estimation The capital asset pricing model can be

considered a specialized case of the arbitrage pricing model, where there is only one

underlying factor and it is completely measured by the market index In general, the CAPM

has the advantage of being a simpler model to estimate and to use, but it will underperform

the richer multi-factor models when an investment is sensitive to economic factors not well

represented in the market index For instance, oil company stocks, which derive most of

their risk from oil price movements, tend to have low CAPM betas and low expected

returns An arbitrage pricing model, where one of the factors may measure oil and other

commodity price movements, will yield a better estimate of risk and higher expected return

for these firms7

Which of these models works the best? Is beta a good proxy for risk and is it

correlated with expected returns? The answers to these questions have been debated widely

in the last two decades The first tests of the CAPM suggested that betas and returns were

positively related, though other measures of risk (such as variance) continued to explain

differences in actual returns This discrepancy was attributed to limitations in the testing

techniques In 1977, Roll, in a seminal critique of the model's tests, suggested that since the

market portfolio could never be observed, the CAPM could never be tested, and all tests of

the CAPM were therefore joint tests of both the model and the market portfolio used in the

tests In other words, all that any test of the CAPM could show was that the model worked

(or did not) given the proxy used for the market portfolio It could therefore be argued that

in any empirical test that claimed to reject the CAPM, the rejection could be of the proxy

used for the market portfolio rather than of the model itself Roll noted that there was no

way to ever prove that the CAPM worked and thus no empirical basis for using the model

Fama and French (1992) examined the relationship between betas and returns

between 1963 and 1990 and concluded that there is no relationship These results have been

contested on three fronts First, Amihud, Christensen, and Mendelson (1992), used the same

data, performed different statistical tests and showed that differences in betas did, in fact,

explain differences in returns during the time period Second, Kothari and Shanken (1995)

estimated betas using annual data, instead of the shorter intervals used in many tests, and

concluded that betas do explain a significant proportion of the differences in returns across

investments Third, Chan and Lakonishok (1993) looked at a much longer time series of

returns from 1926 to 1991 and found that the positive relationship between betas and

returns broke down only in the period after 1982 They also find that betas are a useful

guide to risk in extreme market conditions, with the riskiest firms (the 10% with highest

betas) performing far worse than the market as a whole, in the ten worst months for the

market between 1926 and 1991 (See Figure 2.6)

7 Weston and Copeland used both approaches to estimate the cost of equity for oil companies in 1989 and

came up with 14.4% with the CAPM and 19.1% using the arbitrage pricing model.

FIGURE 2.6: Returns and Betas: Ten Worst Months between 1926 and 1991

High-beta stocks Whole Market Low-beta stocks

While the initial tests of the APM suggested that they might provide more promise

in terms of explaining differences in returns, a distinction has to be drawn between the use

of these models to explain differences in past returns and their use to predict expected

returns in the future The competitors to the CAPM clearly do a much better job at

explaining past returns since they do not constrain themselves to one factor, as the CAPM

does This extension to multiple factors does become more of a problem when we try to

project expected returns into the future, since the betas and premiums of each of these

factors now have to be estimated Because the factor premiums and betas are themselves

volatile, the estimation error may eliminate the benefits that could be gained by moving from

the CAPM to more complex models The regression models that were offered as an

alternative also have an estimation problem, since the variables that work best as proxies for

market risk in one period (such as market capitalization) may not be the ones that work in

the next period

Ultimately, the survival of the capital asset pricing model as the default model for

risk in real world applications is a testament to both its intuitive appeal and the failure of

more complex models to deliver significant improvement in terms of estimating expected

returns We would argue that a judicious use of the capital asset pricing model, without an

over reliance on historical data, is still the most effective way of dealing with risk in modern

corporate finance

Models of Default Risk

The risk that we have discussed hitherto in this chapter relates to cash flows on

investments being different from expected cash flows There are some investments, however,

in which the cash flows are promised when the investment is made This is the case, for

instance, when you lend to a business or buy a corporate bond However, the borrower may

default on interest and principal payments on the borrowing Generally speaking, borrowers

with higher default risk should pay higher interest rates on their borrowing than those with

lower default risk This section examines the measurement of default risk and the

relationship of default risk to interest rates on borrowing

In contrast to the general risk and return models for equity, which evaluate the

effects of market risk on expected returns, models of default risk measure the consequences

of firm-specific default risk on promised returns While diversification can be used to

explain why firm-specific risk will not be priced into expected returns for equities, the same

rationale cannot be applied to securities that have limited upside potential and much greater

downside potential from firm-specific events To see what we mean by limited upside

potential, consider investing in the bond issued by a company The coupons are fixed at the

time of the issue and these coupons represent the promised cash flow on the bond The best

case scenario for you as an investor is that you receive the promised cash flows; you are not

entitled to more than these cash flows even if the company is wildly successful All other

scenarios contain only bad news, though in varying degrees, with the delivered cash flows

being less than the promised cash flows Consequently, the expected return on a corporate

bond is likely to reflect the firm-specific default risk of the firm issuing the bond

The Determinants of Default Risk

The default risk of a firm is a function of two variables The first is the firm’s

capacity to generate cash flows from operations and the second is its financial obligations –

including interest and principal payments8 Firms that generate high cash flows relative to

their financial obligations should have lower default risk than firms that generate low cash

flows relative to their financial obligations Thus, firms with significant existing investments,

which generate relatively high cash flows, will have lower default risk than firms that do not

In addition to the magnitude of a firm’s cash flows, the default risk is also affected by

the volatility in these cash flows The more stability there is in cash flows the lower the

8 Financial obligation refers to any payment that the firm has legally obligated itself to make, such as

interest and principal payments It does not include discretionary cash flows, such as dividend payments or

new capital expenditures, which can be deferred or delayed, without legal consequences, though there may

be economic consequences.

default risk in the firm Firms that operate in predictable and stable businesses will have

lower default risk than will other similar firms that operate in cyclical or volatile businesses

Most models of default risk use financial ratios to measure the cash flow coverage (i.e.,

the magnitude of cash flows relative to obligations) and control for industry effects to

evaluate the variability in cash flows

Bond Ratings and Interest rates

The most widely used measure of a firm's default risk is its bond rating, which is

generally assigned by an independent ratings agency The two best known are Standard and

Poor’s and Moody’s Thousands of companies are rated by these two agencies and their

views carry significant weight with financial markets

The Ratings Process

The process of rating a bond usually starts when the issuing company requests a

rating from a bond ratings agency The ratings agency then collects information from both

publicly available sources, such as financial statements, and the company itself and makes a

decision on the rating If the company disagrees with the rating, it is given the opportunity to

present additional information This process is presented schematically for one ratings

agency, Standard and Poors (S&P), in Figure 2.7

Figure 2.7: The Ratings Process

entered into S&P's administrative and control systems

S&P assigns analyticalteam to issue

Analystsresearch S&P library,internal files and data bases

Issuer meeting: presentation to S&P personnel orS&P personnel tour issuer facilities

Final Analyticalreview and preparation

of rating committeepresentation

to issuer or its authorizedrepresentative

Does issuer wish to appeal

by furnishing additionalinformation?

Presentation of additionalinformation to S&P rating committee:

Discussion and vote to confirm

or modify rating

Formatnotification to issuer or its authorizedrepresentative:Rating is releasedYes

No

THE RATINGS PROCESS

The ratings assigned by these agencies are letter ratings A rating of AAA from Standard

and Poor’s and Aaa from Moody’s represents the highest rating granted to firms that are

viewed as having the lowest default risk As the default risk increases, the ratings decrease

toward D for firms in default (Standard and Poor’s) A rating at or above BBB by Standard

and Poor’s is categorized as investment grade, reflecting the view of the ratings agency that

there is relatively little default risk in investing in bonds issued by these firms

Determinants of Bond Ratings

The bond ratings assigned by ratings agencies are primarily based upon publicly

available information, though private information conveyed by the firm to the rating agency

does play a role The rating assigned to a company's bonds will depend in large part on

financial ratios that measure the capacity of the company to meet debt payments and

generate stable and predictable cash flows While a multitude of financial ratios exist, table

2.1 summarizes some of the key ratios used to measure default risk

Table 2.1: Financial Ratios used to measure Default Risk

Cashflow/ Total Debt

Funds from Operations - Capital Expenditures-Change in Working Capital

Companies with AAA ratings: Take a look at the

companies that commandedtriple AAA ratings fromStandard and Poor’s in themost recent period

Long Term Debt/

There is a strong relationship between the bond rating a company receives and its

performance on these financial ratios Table 2.2 provides a summary of the median ratios9

from 1998 to 2000 for different S&P ratings classes for manufacturing firms

Table 2.2: Financial Ratios by Bond Rating: 1998-2000

Funds flow/total debt 105.8 55.8 46.1 30.5 19.2 9.4 5.8

Free oper cash

Source: Standard and Poors

Note that the pre-tax interest coverage ratio (EBIT) and the EBITDA interest coverage ratio

are stated in terms of times interest earned, whereas the rest of the ratios are stated in

percentage terms

Not surprisingly, firms that generate income and

cash flows significantly higher than debt payments, that

are profitable and that have low debt ratios are more likely

9 See the Standard and Poor’s online site: http://www.standardandpoors.com/ratings/criteria/index.htm

to be highly rated than are firms that do not have these characteristics There will be

individual firms whose ratings are not consistent with their financial ratios, however, because

the ratings agency does add subjective judgments into the final mix Thus, a firm that

performs poorly on financial ratios but is expected to improve its performance dramatically

over the next period may receive a higher rating than is justified by its current financials

For most firms, however, the financial ratios should provide a reasonable basis for guessing

at the bond rating

Synthetic Ratings and Default Risk

Not all firms that borrow money have bond ratings available on them How do you

go about estimating the cost of debt for these firms? There are two choices

• One is to look at recent borrowing history Many firms that are not rated still borrow

money from banks and other financial institutions By looking at the most recent

borrowings made by a firm, you can get a sense of the types of default spreads being

charged the firm and use these spreads to come up with a cost of debt

• The other is to estimate a synthetic rating for the firm, i.e, use the financial ratios used

by the bond ratings agencies to estimate a rating for the firm To do this you would need

to begin with the rated firms and examine the financial characteristics shared by firms

within each ratings class As an example, assume that you have an unrated firm with

operating earnings of $ 100 million and interest expenses of $ 20 million You could

use the interest coverage ratio of 5.00 (100/20) to estimate a bond rating of A- for this

firm.10

Bond Ratings and Interest Rates

The interest rate on a corporate bond should be a function of its default risk, which

is measured by its rating If the rating is a good measure of the default risk, higher rated

bonds should be priced to yield lower interest rates than would lower rated bonds The

difference between the interest rate on a bond with default risk and a default-free

government bond is defined to be the default spread Table 2.3 summarizes default spreads

for 10-year bonds in S&P’s different rating classes as of December 31, 2001:

Table 2.3: Default Spreads and Bond Ratings

10 This rating was based upon a table that was developed in 1999 and 2000, by listing out all rated firms,

with market capitalization lower than $ 2 billion, and their interest coverage ratios, and then sorting firms

based upon their bond ratings The ranges were adjusted to eliminate outliers and to prevent overlapping

ranges.